A Time-Domain Perspective of the Signal Transfer Function of a Continuous-Time $\Delta\Sigma$ Modulator

Abstract

The signal transfer function (STF) of a continuous-time delta sigma modulator (CTDSM) has traditionally been determined using frequency-domain arguments. Unfortunately, the signal flow manipulations used in this process are not valid when the loop filter is periodically time varying, as in the case of modulators with switched-capacitor (SC) or return-to-open (RTO) digital to analog converters (DACs). We present a time-domain technique to determine the STF of a CTDSM, valid irrespective of whether the loop filter is time invariant or time varying. The STFs of first-order modulators with RTO and SC DACs analytically determined whether using our approach is in agreement with results from state-space analysis.